A probability density function verifies more demanding properties than a possibility measure. Probabilistic models ensure a predictable asymptotic behaviour. This should not be taken to suggest possibility theory should not be used. In fact, a histogram is a possibility measure and it is generally a better descriptor of a small sample of data than a probability density function regardless of it...

Fuzzy relation-based models for handling uncertainty (in a non-probabilistic way) in diagnosis problems have been introduced by Sanchez about twenty years ago, and since then applied and developed by several researchers. The paper first reviews the existing proposals, also including the association-based abductive model proposed by Reggia and his co-workers, which uses non-fuzzy relations. A ne...

In this paper we propose a fuzzy TOPSIS (Technique for Order Performance by Similarity to Idea Solution) model using O(m, n)-Trapezoidal Type Fuzzy Number (O(m,n)-Tr.T.F.N.) and possibility theory. An application in the form of an example to the vendor selection problem in supply chain management is presented towards the end of the paper to highlight the salient points in the proposed possibili...

This paper proposes a general discussion of the handling of imprecise and uncertain information in temporal reasoning in the framework of fuzzy sets and possibility theory. The introduction of fuzzy features in temporal reasoning can be related to different issues. First, it can be motivated by the need of a gradual, linguistic-like description of temporal relations even in the face of complete...

The main subject of this paper is the embedding of fuzzy set theory—and related concepts—in a coherent conditional probability scenario. This allows to deal with perception-based information—in the sense of Zadeh—and with a rigorous treatment of the concept of likelihood, dealing also with its role in statistical inference. A coherent conditional probability is looked on as a general non-additi...

This paper is an attempt to cast both uncertainty and time in a logical framework. It generalizes possibilistic logic, previously developed by the authors, where each classical formula is associated with a weight which obeys the laws of possibility theory. In the possibilistic temporal logic we present here, each formula is associated with a time set (a fuzzy set in the more general case) which...

Uncertainty is present in virtually all replacement decisions due to unknown future events, such as revenue streams, maintenance costs, and in°ation. Fuzzy sets provide a mathematical framework for explicitly incorporating imprecision into the decision-making model, especially when the system involves human subjectivity. This chapter illustrates the use of fuzzy sets and possibility theory to e...

In safety, reliability as well as risk analysis and management, information often is uncertain and imprecise. The approach to air incident analysis under uncertain and imprecise information presented in our paper is inspired by the possibility theory. Notably, in such analyses these are both: static and dynamic components that have to be included. As part of this work, static analysis of a seri...

1. Gradualness: the idea that many categories in natural language are a matter of degree, including truth. The extension of a gradual predicate is a fuzzy set, a set where the transition between membership and non-membership is gradual rather than abrupt. This is Zadeh’s original intuition [29]. 2. Epistemic Uncertainty: the idea of partial or incomplete information. In its most primitive form,...

Interval-valued fuzzy sets were proposed thirty years ago as a natural extension of fuzzy sets. Many variants of these mathematical objects exist, under various names. One popular variant proposed by Atanassov starts by the specification of membership and non-membership functions. This paper focuses on interpretations of such extensions of fuzzy sets, whereby the two membership functions that d...